I took AP World in my sophomore year, but we didn't even use a textbook in class. I got the AP World review book by the Princeton Review, studied the heck out of it, and got a 5 on the AP. A textbook will help, but for me, it wasn't necessary. For me, the review book gave me enough info to get a 5.
imo, the multiple choice questions don't require you to know a lot of minor details, just a good understanding of what's going on in the world at any given period.